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Theorems · Theorem · order theory

Set.PartiallyWellOrderedOn.union

∀ {α : Type u_2} {r : α → α → Prop} {s t : Set α},
  s.PartiallyWellOrderedOn r → t.PartiallyWellOrderedOn r → (s ∪ t).PartiallyWellOrderedOn r
Defined in
Mathlib.Order.WellFoundedSet
Cited by
2 results in Mathlib
Foundations
Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.IsPWO.union · cited by 2IsPWO.unionSet.partiallyWellOrderedOn_union · cited by 1Set.partiallyWellOrderedO…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetOrderEmbedding · cited by 619OrderEmbeddingSet.PartiallyWellOrderedOn · cited by 34Set.PartiallyWellOrderedOnOrderEmbedding.strictMono · cited by 26OrderEmbedding.strictMonoSet.PartiallyWellOrderedOn.exists_lt · cited by 3PartiallyWellOrderedOn.ex…Nat.exists_subseq_of_forall_mem_union · cited by 2Nat.exists_subseq_of_fora…PartiallyWellOrderedOn.unionCITED BYCITES

Cites7

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Cited by2

Results whose statement or proof uses this declaration.